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On solving atomic structures using X-rays

If you can produce crystals of a molecule or other chemical species (e.g. something as 'simple' as a diamond and going all the way to constituent molecules of viruses), you may be able to determine its atomic structure!

You can do so by directing a beam of X-rays at it and observing how strongly and in what directions the X-ray photons are diffracted (e.g. using a CCD detector similar to the one used in ordinary cameras). The method is called X-ray crystallography. However, before we can solve the structure, we have to overcome a few problems. One major problem is that a crucial part of the information is irretrievably lost in the experiment. This has to do with the relative phases of diffracted beams (there are no detectors for these phase differences). Over the past century or so, ingenious ways have been devised to solve or at least get around this "phase problem."

One way of getting around the problem would be to use lenses that recombine the diffracted beams in appropriate phase relationships to produce an image of the object being observed. This is basically how a light microscope works. However, the technology for good enough lenses for X-ray photons is not available either. So how to do the light microscopy trick without the benefit of lenses? If we could somehow figure out the phases, we can solve the structure mathematically!

One method of solving the phase problem is called molecular replacement. If a known structure (called the "search model") is thought to be similar to the unknown ("target") structure, then an attempt can be made to properly place and orient the search model, or a part of it, in the target crystal. Ideally, after this step, phases calculated from this atomic model can be combined with the intensity and direction data of the target to calculate an initial electronic density map. Attempts are now made to better this initial atomic model. One way of doing that is by making manual corrections to it so it fits the electron density better. An improved model implies improvement in phases for the next round of electron density calculation, leading, in turn, to further improvements in the model. These cycles are repeated until no significant improvements can economically be made.

But that's more or less the ideal case. What if the search model is too dissimilar to the target model (e.g. less than 30% sequence identity between the target and search models in case of proteins)? In this case, errors in the initial electron density can be so large that it can be difficult, if not impossible, to improve an even correctly placed search model. (This is because then it's difficult to tell what's real and what is just biased information--a problem not altogether different from that encountered in a few other areas of human endeavors!) The phases, you see, are very important. And these never came from the experiment itself but only from some structure that we assumed to be similar enough to the target. And we can be wrong in our assumptions!

How could we use the least amount of phase information to solve macromolecular (large molecule) structures? This is a major research area in macromolecular crystallography. This was also a problem we faced in trying to solve the first structure of an enzyme called sulfamidase.

If I got you a bit intrigued about how atomic structures are solved in general using X-ray crystallography or about how difficult molecular replacement problems such as this can sometimes be overcome, you might like to check out a bit more detailed (but hopefully also understandable) account than this, e.g. the freely accessible Introduction and Sulfamidase sections of this writeup. The sulfamidase structure was solved and has been published.

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